An Introduction to G-Convergence

Front Cover
Springer Science & Business Media, 1993 - Mathematics - 340 pages
The last twentyfive years have seen an increasing interest for variational convergences and for their applications to different fields, like homogenization theory, phase transitions, singular perturbations, boundary value problems in wildly perturbed domains, approximation of variatonal problems, and non­ smooth analysis. Among variational convergences, De Giorgi's r-convergence plays a cen­ tral role for its compactness properties and for the large number of results concerning r -limits of integral functionals. Moreover, almost all other varia­ tional convergences can be easily expressed in the language of r -convergence. This text originates from the notes of the courses on r -convergence held by the author in Trieste at the International School for Advanced Studies (S. I. S. S. A. ) during the academic years 1983-84,1986-87, 1990-91, and in Rome at the Istituto Nazionale di Alta Matematica (I. N. D. A. M. ) during the spring of 1987. This text is far from being a treatise on r -convergence and its appli­ cations.

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Contents

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IV
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VI
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VII
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XXIX
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XXXI
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XXXIII
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XXXV
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XXXVII
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XXXIX
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Page 330 - An approach for constructing families of homogenized equations for periodic media. I: An integral representation and its consequences.
Page 319 - Mathematical aspects of the physics of disordered systems. Critical phenomena, random systems, gauge theories, Proc. Summer Sch. Theor. Phys., Sess. 43, Les Houches/France 1984, Pt.
Page 327 - Un teorema di passaggio al limite per la somma di funzioni convesse, Boll.
Page 330 - Cont re-examples pour divers problemes ou le controle intervient dans les coefficients.
Page 332 - On an elaboration of M. Kac's theorem concerning eigenvalues of the Laplacian in a region with randomly distributed small obstacles.
Page 317 - J.-L. (Eds.), Homogenization and Effective Moduli of Materials and Media. The IMA Volumes in Mathematics and Its Applications (Springer, Berlin, 1986), pp. 1-26. [6] Bends0e, MP , "Optimal Shape Design as a Material Distribution Problem".

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